An evaluation of fitting methods for the sum of two hyperbolas: application to uptake studies

Measuring affinities of fission yeast spindle pole body proteins in live cells across the cell cycle

Characterizing protein-protein interactions is essential for understanding molecular mechanisms, although reproducing cellular conditions in vitro is challenging and some proteins are difficult to purify. We developed a method to measure binding to cellular structures using fission yeast cells as reaction vessels. We varied the concentrations of Sid2p and Mob1p (proteins of the septation initiation network) and measured their binding to spindle pole bodies (SPBs), the centrosome equivalent of yeast. From our measurements we infer that Sid2p and Mob1p both exist as monomeric, heterodimeric, and homodimeric species throughout the cell cycle. During interphase these species have widely different affinities for their common receptor Cdc11p on the SPB. The data support a model with a subset of Cdc11p binding the heterodimeric species with a Kd < 0.1 μM when Sid2p binds Mob1p-Cdc11p and Kd in the micromolar range when Mob1p binds Sid2p-Cdc11p. During mitosis an additional species presumed to be the phosphorylated Sid2p-Mob1p heterodimer binds SPBs with a lower affinity. Homodimers of Sid2p or Mob1p bind to the rest of Cdc11p at SPBs with lower affinity: Kds > 10 μM during interphase and somewhat stronger during mitosis. These measurements allowed us to account for the fluctuations in Sid2p binding to SPBs throughout the cell cycle.

Uptake of selenite by Saccharomyces cerevisiae involves the high and low affinity orthophosphate transporters

Although the general cytotoxicity of selenite is well established, the mechanism by which this compound crosses cellular membranes is still unknown. Here, we show that in Saccharomyces cerevisiae, the transport system used opportunistically by selenite depends on the phosphate concentration in the growth medium. Both the high and low affinity phosphate transporters are involved in selenite uptake. When cells are grown at low P(i) concentrations, the high affinity phosphate transporter Pho84p is the major contributor to selenite uptake. When phosphate is abundant, selenite is internalized through the low affinity P(i) transporters (Pho87p, Pho90p, and Pho91p). Accordingly, inactivation of the high affinity phosphate transporter Pho84p results in increased resistance to selenite and reduced uptake in low P(i) medium, whereas deletion of SPL2, a negative regulator of low affinity phosphate uptake, results in exacerbated sensitivity to selenite. Measurements of the kinetic parameters for selenite and phosphate uptake demonstrate that there is a competition between phosphate and selenite ions for both P(i) transport systems. In addition, our results indicate that Pho84p is very selective for phosphate as compared with selenite, whereas the low affinity transporters discriminate less efficiently between the two ions. The properties of phosphate and selenite transport enable us to propose an explanation to the paradoxical increase of selenite toxicity when phosphate concentration in the growth medium is raised above 1 mm.

A kinetic analysis of the actions of L-noradrenaline and its related agonists and antagonists on in vitro lipolysis in rat adipose tissue

(1) Iterative non-linearising optimisation techniques have been used to fit three alternative models to relationships between beta-adrenergic effector concentrations and the lipolytic response which they elicit in dispersed adipocytes derived from rat epididymal fat pads. (2) The models, which consist of a simple hyperbolic relationship, a Hill-type functions and a rational quadratic formulation, were fitted to data obtained with agonists, "partial" agonists and antagonists both alone and in combination. (3) Whereas the hyperbolic relationship was inadequate in all circumstances, the hill-type function accommodated dose-response curves which exhibit no "auto-inhibitory" hook or bell-shaped feature. However, the rational quadratic function could be satisfactorily fitted to the data whether or not the auto-inhibitory phase was apparent. (4) The mechanisms that govern the steepness of the dose-response relationships and their bell-shaped feature are discussed. Evidence is presented that the latter originates at the level of adenylate cyclase.

The application of robust non-linear regression methods for fitting hyperbolic Scatchard plots

The Scatchard plot is an essential tool for the estimation of binding parameters in biochemistry. In certain situations the fitting of a hyperbolic line is required in this context. It is proposed to solve this non-linear regression problem by robust methods. A method according to Huber and Dutter (1974) is outlined and its good applicability is demonstrated.